The necessity of torsion in gravity

摘要

It is shown that torsion is required for a complete theory of graviation, and that without it, the equations of gravitation violate fundamental laws. In the first case, we are reminded that, in the absence of external forces, the correct conservation law of total angular momentum arises only if torsion, whose origin is intrinsic spin, is included into gravitation. The second case considers the "mass reversal" transformation. It has been known that under a global chiral transformation and "mass to negative mass" transformation, the Dirac equation is invariant. But global transformations violate special relativity, so this transformation must be made local. It is shown that the torsion is the gauge field for this local invariance.